Estimating the amplitude of measurement noise present in chaotic time series

Chaos

Volumn 9, Issue 2, 1999, Pages 436-444

  Tanaka, Naoki ^a   Okamoto, Hiroshi ^a   Naito, Masayoshi ^a  

^a HITACHI LTD   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039726692     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.166418     Document Type: Article

References (26)

1. J.-P. Eckmann and D. Ruelle, Rev. Mod. Phys. 57, 617 (1985).
2. H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. Sh. Tsimring, Rev. Mod. Phys. 65, 1331 (1993).
3. E. J. Kostelich and J. A. Yorke, Physica D 41, 183 (1990).
4. P. Grassberger and T. Schreiber, Int. J. Bifurcation Chaos Appl. Sci. Eng. 1, 521 (1991).
5. M. Sano and Y. Sawada, Phys. Rev. Lett. 55, 1082 (1985).
6. T. Schreiber, Phys. Rev. E 47, 2401 (1993).
7. R. Cawley and G.-H. Hsu, Phys. Rev. A 46, 3057 (1992).
8. S. M. Hammel, Phys. Lett. A 148, 421 (1990).
9. P. Bergé, Y. Pomeau, and Ch. Vidal, L'Odre dans le Chaos (Hermann, Paris, 1984), Chap. 3.
10. J. Guckenheimer, Nature (London) 298, 358 (1982).
11. A. Ben-Mizrachi, I. Procaccia, and P. Grassberger, Phys. Rev. A 29, 975 (1984).
12. T. Schreiber, Phys. Rev. E 48, R13 (1993).
13. C. J. Cellucci, A. M. Albano, R. E. Rapp, R. A. Pittenger, and R. O. Josiassen, Chaos 7, 414 (1997).
14. J. D. Farmer and J. J. Sidorowich, Phys. Rev. Lett. 59, 845 (1987).
15. M. Casdagli, Physica D 35, 335 (1989).
16. G. Sugihara and R. M. May, Nature (London) 344, 734 (1990).
17. D. J. Wales, Nature (London) 350, 485 (1991).
18. F. Takens, in Dynamical System and Turbulence, edited by D. A. Rand and L.-S. Young, Lecture Notes in Mathematics, Vol. 898, p. 366 (Springer-Verlag, Berlin, 1981).
19. M. Casdagli, S. Eubank, J. D. Farmer, and J. Gibson, Physica D 51, 52 (1991).
20. T. Sauer, J. A. Yorke, and M. Casdagli, J. Stat. Phys. 65, 579 (1991).
21. N. Tanaka, H. Okamoto, and M. Naito, Jpn. J. Appl. Phys., Part 1 34, 388 (1995).
22. 2〉 appearing in Eq. (11).
23. M. Hénon, Commun. Math. Phys. 50, 69 (1976).
24. K. Ikeda, Opt. Commun. 30, 257 (1979).
25. E. N. Lorenz, J. Atmos. Sci. 20, 130 (1963).
26. H. Okamoto, N. Tanaka, and M. Naito, J. Phys. Chem. A 101, 8480 (1997).